University of Illinois Urbana-Champaign

Topics in analytic number theory

Jaffe, Grace Natalie

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JAFFE-DISSERTATION-2023.pdf

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https://hdl.handle.net/2142/120085

Description

Title
Topics in analytic number theory
Author(s)
Jaffe, Grace Natalie
Issue Date
2023-04-28
Director of Research (if dissertation) or Advisor (if thesis)
  • Reznick, Bruce
  • Zaharescu, Alexandru
Doctoral Committee Chair(s)
Berndt, Bruce C
Committee Member(s)
Nath, Kunjakanan
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • number theory
  • Frobenius problem
  • Stern sequence
  • Farey sequences
  • Dirichlet L-function
  • Riemann zeta function
Abstract
In Part I of this thesis, we show that for relatively prime positive integers a,b, there is a maximum integer g(a,b) which is not expressible as ax+by for x,y non-negative, relatively prime integers. We then explore the connections between this quantity and the Frobenius problem, Farey sequence, and Stern sequence. In Part II, we consider the zeros of a polynomial in derivatives of a Dirichlet L-function and give an asymptotic formula for the number of zeros with imaginary part between 1 and large T.
Graduation Semester
2023-05
Type of Resource
Thesis
Handle URL
https://hdl.handle.net/2142/120085
Copyright and License Information
Copyright 2023 Grace Jaffe

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Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois